The generator matrix

 1  0  0  0  1  1  1 2X  1  1  1  1  1  1 2X  1  1  1 2X 2X  1 2X  1  1  1  X 2X  X  1  1  1  1  1  1  0  X  1  1  1  1  1  1  1  1  1
 0  1  0  0  0  1 2X+1  1  X  X 2X+2 X+2 2X 2X 2X X+1 2X+1 X+2  1  1  2  1  1  X  1  1  1  1  2 X+1 2X  X X+1 2X+2  1  1 2X 2X+1 X+2  X X+1 2X+1 2X+1  2  0
 0  0  1  0  1  1 2X+2 2X+1 2X+1 X+2  X 2X+1  X X+2  1 2X  0 X+2 2X+2 X+2 2X+2 2X+2 2X+1  2 X+1  0  1  0 X+2  2 2X 2X+1  2 2X+1  X  1  X X+2 2X X+2  0 2X X+1 X+1  X
 0  0  0  1  2  X 2X+2 2X+2 X+1  0  1  X 2X+2  1 2X+1  2  X  0 2X 2X+2 2X+1 X+1  1  2 X+2  2  0 2X+2 2X  0 X+1 2X 2X X+1  0 X+1 2X+2 2X+1  2  1 2X+1  1 2X+1 2X+1  X
 0  0  0  0 2X  0 2X 2X  X 2X 2X 2X  X  0 2X 2X  X  X 2X  0  0  0  X  X  X  X  X  0  0  X  0  0 2X  0 2X  0 2X  0  X  X 2X  X  0 2X  X

generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+128x^78+246x^79+216x^80+612x^81+936x^82+516x^83+772x^84+1260x^85+678x^86+1040x^87+1608x^88+900x^89+1322x^90+1734x^91+912x^92+1190x^93+1530x^94+660x^95+894x^96+918x^97+396x^98+466x^99+426x^100+84x^101+106x^102+90x^103+12x^104+24x^105+2x^108+2x^111+2x^114

The gray image is a linear code over GF(3) with n=135, k=9 and d=78.
This code was found by Heurico 1.16 in 4.81 seconds.